assign vs lay claim

assign and lay claim both are verbs.

Word	Noun	Adjective	Verb	Adverb
assign	No	No	Yes	No
lay claim	No	No	Yes	No

As verbs, lay claim is a hypernym of assign; that is, lay claim is a word with a broader meaning than assign:

assign: make undue claims to having
lay claim: demand as being one's due or property; assert one's right or title to

Other hypernyms of assign include arrogate, claim.

assign (verb)	lay claim (verb)
select something or someone for a specific purpose	demand as being one's due or property; assert one's right or title to
attribute or credit to
decide as to where something belongs in a scheme
attribute or give
transfer one's right to
give out
make undue claims to having
give an assignment to (a person) to a post, or assign a task to (a person)